Skip to main content
×
×
Home

Modelling heterogeneity in survival data

  • Philip Hougaard (a1)
Abstract

Ordinary survival models implicitly assume that all individuals in a group have the same risk of death. It may, however, be relevant to consider the group as heterogeneous, i.e. a mixture of individuals with different risks. For example, after an operation each individual may have constant hazard of death. If risk factors are not included, the group shows decreasing hazard. This offers two fundamentally different interpretations of the same data. For instance, Weibull distributions with shape parameter less than 1 can be generated as mixtures of constant individual hazards. In a proportional hazards model, neglect of a subset of the important covariates leads to biased estimates of the other regression coefficients. Different choices of distributions for the unobserved covariates are discussed, including binary, gamma, inverse Gaussian and positive stable distributions, which show both qualitative and quantitative differences. For instance, the heterogeneity distribution can be either identifiable or unidentifiable. Both mathematical and interpretational consequences of the choice of distribution are considered. Heterogeneity can be evaluated by the variance of the logarithm of the mixture distribution. Examples include occupational mortality, myocardial infarction and diabetes.

Copyright
Corresponding author
Postal address: Biostatistical Department, Novo Research Institute, Novo Alle, 2880 Bagsværd, Denmark.
References
Hide All
Aalen, O. O. (1988) Heterogeneity in survival analysis. Statist. Med. 7, 11211137.
Andersen, O. (1985) Dødelighed og erhverv 1970–80. Danmarks Statistik, Copenhagen, Denmark.
Bar-Lev, S. K. and Enis, P. (1986) Reproducibility and natural exponential families with power variance functions. Ann. Statist. 14, 15071522.
Borch–Johnsen, K., Andersen, P. K. and Deckert, T. (1985) The effect of proteinuria on relative mortality in Type 1 (insulin-dependent) diabetes mellitus. Diabetologia 28, 590596.
Heckman, J. J. and Singer, B. (1982) The identification problem in econometric models for duration data. In Advances in Econometrics, ed. Hildenbrand, W., Cambridge, pp. 3977.
Hougaard, P. (1986) Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387396.
Hougaard, P. (1987) Modelling multivariate survival. Scand. J. Statist. 14, 291304.
Jørgensen, B. (1987). Exponential dispersion models. J. R. Statist. Soc. B 49, 127162.
Manton, K. G., Stallard, E. and Vaupel, J. W. (1986) Alternative models for the heterogeneity of mortality risks among the aged. J. Amer. Statist. Assoc. 81, 635644.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 10 *
Loading metrics...

Abstract views

Total abstract views: 169 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd August 2018. This data will be updated every 24 hours.